Number Series, Coding-Decoding & Odd Man Out Practice Test - Quant Aptitude

Each term follows the formula n3 - n, for n = 1, 2, 3, 4, 5, 6:

13-1=0, 23-2=6, 33-3=24, 43-4=60, 53-5=120, 63-6=210.

The next term (n=7): 73-7 = 343-7 = 336.

Each term follows the formula n2 + 1, for n = 1, 2, 3, ...:

12+1=2, 22+1=5, 32+1=10, 42+1=17, 52+1=26, 62+1=37, 72+1=50, and 82+1=65.

The 8th term should be 65, but the series shows 64, breaking the pattern -- so 64 is the odd one out.

Compare each letter of MADRAS with the coded NBESBT: M→N, A→B, D→E, R→S, A→B, S→T. Every letter is simply shifted forward by 1 in the alphabet.

Applying the same +1 shift to DELHI: D→E, E→F, L→M, H→I, I→J, giving EFMIJ.

Comparing GLAMOUR→IJCNMWP letter by letter (by alphabet position) gives a repeating shift pattern applied to each of the 7 letter-positions: +2, -2, +2, +1, -2, +2, -2. The same pattern applied to MISRULE→OGUSSNC confirms this rule.

Applying this same position-wise shift pattern to MUSICAL (M, U, S, I, C, A, L):

M(+2)=O, U(-2)=S, S(+2)=U, I(+1)=J, C(-2)=A, A(+2)=C, L(-2)=J.

Result: OSUJACJ.

Each of 50, 82, 170 and 290 is exactly 1 more than the square of an odd number: 50 = 72+1, 82 = 92+1, 170 = 132+1, 290 = 172+1.

48, however, does not fit this pattern -- 48-1 = 47, which is not a perfect square. So 48 is the term that breaks the series.

Check the gaps between consecutive letters in each group:

CEHL: C→E (+2), E→H (+3), H→L (+4) -- gaps 2, 3, 4.

KMPT: K→M (+2), M→P (+3), P→T (+4) -- gaps 2, 3, 4.

OQTX: O→Q (+2), Q→T (+3), T→X (+4) -- gaps 2, 3, 4.

NPSV: N→P (+2), P→S (+3), S→V (+3) -- gaps 2, 3, 3, breaking the +2, +3, +4 pattern followed by the other three.

So NPSV is the odd one out.

All the other numbers in the series (7, 11, 13, 19, 23) are prime numbers.

15 = 3 × 5 is not prime, so it is the odd one out.

Check the differences between consecutive terms: 7-1=6, 17-7=10, 31-17=14, 49-31=18, 71-49=22.

The differences themselves increase by 4 each time: 6, 10, 14, 18, 22, so the next difference is 26.

Next term = 71 + 26 = 97.

From PAINT = 74128: P=7, A=4, I=1, N=2, T=8.

From ACCEPT = 455978: A=4, C=5, C=5, E=9, P=7, T=8 (confirms A=4, P=7, T=8).

So the code letters are: P=7, A=4, T=8, I=1, E=9, N=2, T=8.

PATIENT = P-A-T-I-E-N-T = 7-4-8-1-9-2-8 = 7481928.

Compare MONKEY with its code NNOJFX letter by letter:

M(+1)→N, O(-1)→N, N(+1)→O, K(-1)→J, E(+1)→F, Y(-1)→X.

The pattern alternates +1, -1, +1, -1, +1, -1 for successive letters.

Applying the same alternating pattern to PUZZLE: P(+1)→Q, U(-1)→T, Z(+1)→A (wrapping past Z to A), Z(-1)→Y, L(+1)→M, E(-1)→D.

Code = QTAYMD.

Check the differences between consecutive terms: 12-11=1, 14-12=2, 17-14=3, 22-17=5, 30-22=8.

The differences themselves form a Fibonacci-like pattern: 1, 2, 3, 5, 8, where each difference is the sum of the two before it, so the next difference is 5 + 8 = 13.

Next term = 30 + 13 = 43.

From DOCTOR = 423527: D=4, O=2, C=3, T=5, O=2, R=7.

From PATIENT = 8651905: P=8, A=6, T=5 (confirms T=5), I=1, E=9, N=0, T=5.

So the code letters are: O=2, P=8, E=9, R=7, A=6, T=5, I=1, N=0.

OPERATION = O-P-E-R-A-T-I-O-N = 2-8-9-7-6-5-1-2-0 = 289765120.

From CODE = 1357: C=1, O=3, D=5, E=7.

From GAMER = 24678: G=2, A=4, M=6, E=7 (confirms E=7), R=8.

So the code digits are: R=8, A=4, C=1, E=7.

84178 = 8-4-1-7-8 = R-A-C-E-R = RACER.

Comparing SUBJECT with UWDLGEV letter by letter: S→U, U→W, B→D, J→L, E→G, C→E, T→V -- every letter is shifted forward by exactly 2 positions in the alphabet.

Applying the same +2 shift to MENTION: M→O, E→G, N→P, T→V, I→K, O→Q, N→P.

Code = OGPVKQP.

Each term is obtained from the previous term by multiplying by an increasing integer and adding that same integer:

7 × 1 + 1 = 8. 8 × 2 + 2 = 18. 18 × 3 + 3 = 57. 57 × 4 + 4 = 232. 232 × 5 + 5 = 1165.

Next: 1165 × 6 + 6 = 6990 + 6 = 6996.